Question

In an annual report to investors, an investment firm claims that the share price of one of their bond funds had very little variability. The report shows the average price as $⁢17.00 with a variance of 0.11. One of the investors wants to investigate this claim. He takes a random sample of the share prices for 11 days throughout the last year and finds that the standard deviation of the share price is 0.1626. Can the investor conclude that the variance of the share price of the bond fund is different than claimed at α=0.05? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

H0:

Ha:

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision.

A. Reject Null Hypothesis

B. Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion?

A. There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

B. There is not sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.3317
Alternative Hypothesis, Ha: σ ≠ 0.3317

2)

Rejection Region
This is two tailed test, for α = 0.05 and df = 10
Critical value of Χ^2 are (3.247, 20.483)

Hence reject H0 if Χ^2 < 3.247 or Χ^2 > 20.483

3)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (11 - 1)*0.1626^2/0.3317^2
Χ^2 = 2.403

4)

A. Reject Null Hypothesis

5)

A. There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.